Tagged Questions

Mathematical intuition is the instinctive impression regarding mathematical ideas which originate naturally without regard to formal mathematical proofs. It may or may not stem from a cognitive rational process.

Suppose I had some linear function $f(x)$ and then I sampled the function over the integers to form $f(n)$, what would be the evaluation of the Lebesgue integral of $\int_\mathbb{Z_+} f(n) d\mu$?
For ...

In this informative and concise set of notes on vanishing cycles by Donu Arapura, it is stated that the theory of vanishing cycles ports nicely to the etale world if the role of the disk is replaced ...

I just had a really quick question to ask. I was reading a book on linear algebra and have just been trying to wrap my head around what exactly a matrix represents. At one point, the book said
"In a ...

I'm sorry if this question makes no sense. I have been reading generatingfunctionology and I have been able to solve the problems in the first chapters and I understand the mechanism I have to follow ...

I am reading this text http://www.math-cs.gordon.edu/courses/ma225/handouts/sepvar.pdf to justify the method to solve first order seperable differentiable equations, where we are told first told that: ...

In very different contexts of mathematical physics (rigid body mechanics, fluidodynamics, general relativity, quantum field theory,...) I have come across the following expression:
$$
A^tA-AA^t,
$$
...

Find an expression for $\frac {\partial B} {\partial T}$ applied to the Black-Body radiation law by Planck:
$$B(f,T)=\frac{2hf^3}{c^2\left(\exp\frac{hf}{kT}-1\right)}$$
The correct answer is $\frac ...

When treating division as "groups of the numerator" (sorry, I don't know the technical term -- see image), why does a complex fraction in the denominator get added together to produce a 1 (number of ...

I am trying to understand the motivation behind defining stalks of sheaves, but I suppose my complex geometry is a little weak. I know they are meant to represent germs of holomorphic functions at a ...

I am trying to understand the intuition of thinking about number theoretic ideas in terms of geometric ones. For example, ramification is something that happens when a "covering" space of a Riemann ...

Let $p:E\to B$ be a smooth fiber bundle with fiber $F$. Consider the vector spaces $V_u=\{x\in T_uE: p_*(x)=0\}$. We call $V_u$ the vertical subspace of the tangent space $T_uE$.
How can we see that ...

i was having a tough time deciding on which SE site to post this rather unique question being that it would help me with a program I'm writing. I decided to come to you guys, not hoping that you would ...

Question: Let $K$ be a number field. The proper intuitive motivation for the ring of integers $\mathcal O_K$ is that $\mathbb Z$ is to $\mathbb Q$ as $\mathcal O_K$ is to $K$. But what plays the role ...

This question is concerned with the algebraic side of the theory of prolongations as explained in this paper by V. Guillemin and S. Sternberg. Let me first introduce my notation.
We're working with a ...

We know the SHM differential equation is of second-order $$\dfrac{d^2 x}{dt^2} = -{\omega}^2 x$$ . So, the solution of this equation must contain two arbitrary constants. And also we know that $x = ...

In "Counter-examples in topology" of Steen and Seebach, they define a filter on a set $X$ is a collection F of subsets of $X$ with the following properties:
Every subset of $X$ which contains a set ...